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mtsm
Posts: 78
Joined: July 28th, 2010, 1:40 pm

Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 28th, 2017, 12:25 am

Other than that, I can see a lot of reasons why you would want to have better curves than what you describe. 
Can you name any of those reasons?
The only problem I am seeing with what you describe is that you might want to express n-1 of your curves as spreads to one base curve.
Good point. I think in theory it doesn't really matter wether you express all curve delta individually or as one base curve per currency with the remaining curves being spread curves over that principle curve. In practice, as curves in one currency tend to strongly move together, I guess the second alternative saves you some hedging and bid-ask-spread.
If you have a not overly sophisticated crowd at your end, what you say is probably OK.
What would a (very) sophisticated crowd demand? For OIS curves obviously central bank meeting dates - but this works with a straightforward Interpolation method as well, doesn't it? Libor curves I may want to model as spread curves. I guess there is a lot more stuff I'm missing out here, which I'm very interested in :-)
With regards to absence of arbitrage in models, I was simply saying that there are some real situations where you can add value to a business, but which would be difficult to achieve in an arbitrage free context. The "bleeding to death" argument is textbook. I am not even going to respond to that. It's a very theoretical argument and dealer books with toxic legacy sh!t in them often have other worries. 
I was mostly thinking about more creative curves building. You may want to incorporate some serious micro-structure into your curves, non standard stuff if you have a well defined view. Or another example is curves built off very few instruments, like take a single fly for example. And you don't want to do some stupid textbooky thingy and use a NS model or something.Then interpolation suddenly is everything. 
I don't actually agree with what you say about expressing curve deltas individually. Again, the main issue is that you need to see an actual book in action. Rates products are highly redundant in that they all express a notion of bulk interest rate and then there is basis on top. In any given market you use only the very much most liquid instruments to hedge away your exposure and then maybe you do a basis hedge once in a while. If you have risk scattered across vraious instruments it's not very nice. Then you have to be creative, like BBG in their ICVS risk. If you can avoid that, it's much better.
 
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Gamal
Posts: 1284
Joined: February 26th, 2004, 8:41 am

Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 28th, 2017, 10:58 am

You are just wrong about that Gamal. Absence of arbitrage is very much a theoretical concept. Most of the time you would not even be able to observe it. It's just not necessarily the way a real market works. Of course if you live in this silly quant world and you believe that rates and vols just exist and are tied together by some idealized contraints, I can't help. But that's not the way things work. Not my main point though. 

The problem is that most arbitrage free models are overly constrained (dynamically) and too complex. I am only saying that you can achieve something more practically useful if you neglect absence of arbitrage. Depends on your usage of course.
There's a gap between "being absolutely orthodox about arbitrage models" and "no care about arbitrage opportunities." If your trading model has got arbitrage opportunities, your trading partners will spot it and rob you blind faster than you may expect.
 
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Paul
Posts: 6604
Joined: July 20th, 2001, 3:28 pm

Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

March 28th, 2017, 12:58 pm

There are many different types of arbitrage. Unless you are more precise this is all meaningless.
 
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arkestra
Posts: 2
Joined: November 25th, 2005, 9:59 am

Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

May 22nd, 2017, 10:59 pm

It depends what you're doing.

If you are doing a large swap portfolio unwind, involving lots of seasoned deals, in the context of some kind of multilateral program (Trioptima etc) then you need to spline to get a sensible level of projected forwards. If you don't do this, then imperfections in your forward curve will be crystallised as a loss to you.

Come to think of it, I guess the same is somewhat true of general off-par market making.

A useful exercise is to look at the structure of the forward rates on a daily resolution, and reflect on whether they are laying you open to under/overpricing.
 
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BerndSchmitz
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Joined: August 16th, 2011, 9:48 am

Re: (discount and forward) curve interpolation - sophisticated methods or keep it simple?

May 24th, 2017, 7:38 am

Hi arkestra,

what exactly do you mean by "imperfections in the forward curve". If you choose to interpolate linearly directly on the forwardLiborRates then your forwardLiborRates look, well, linearly interpolated :-). I wouldn't call this imperfect and consider it a valid Interpolation method, wouldn't you? Obviously I would then also benchmark this method against the market, i.e. calibrate the curve to the set of calibration instruments that I deem liquid and look at the implied rate for less liquid tenors. Hopefully they match to what is published on Reuters etc.

Bernd